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Tridiagonalization of completely nonnegative matrices


Authors: J. W. Rainey and G. J. Habetler
Journal: Math. Comp. 26 (1972), 121-128
MSC: Primary 65F15
DOI: https://doi.org/10.1090/S0025-5718-1972-0309290-8
MathSciNet review: 0309290
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Abstract: Let $ M = [{m_{ij}}]_{i,j = 1}^n$ be completely nonnegative (CNN), i.e., every minor of $ M$ is nonnegative. Two methods for reducing the eigenvalue problem for $ M$ to that of a CNN, tridiagonal matrix, $ T = [{t_{ij}}]$ ( $ {t_{ij}} = 0$ when $ \vert i - j\vert > 1)$), are presented in this paper. In the particular case that $ M$ is nonsingular it is shown for one of the methods that there exists a CNN nonsingular $ S$ such that $ SM = TS$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1972-0309290-8
Keywords: Tridiagonalization, tridiagonal matrices, completely nonnegative matrices, Hessenberg matrices
Article copyright: © Copyright 1972 American Mathematical Society